The Federal Reserve plans to deliver results of stress tests on U.S. banks to executives today that may show about 10 companies need additional capital to weather a deeper recession, people familiar with the matter said.

Banks are formulating plans for filling their capital requirements, much of which would likely come from conversions of preferred shares, the people said. Many of the 19 lenders under review and the government are set to discuss publicly the examinations after markets close May 7, the people said.

Financial shares jumped the most in almost a month yesterday on optimism about the tests. The Treasury and regulators have presented different options for the banks to shore up their books without taking taxpayer money, including selling assets, seeking private capital and converting previous government investments from preferred to common shares.

“Maybe the capital that’s required from these tests is going to be smaller than the market had been anticipating,” said Blake Howells, an analyst at Becker Capital Management, which oversees $1.7 billion in Portland, Oregon, and owns shares of U.S. Bancorp and KeyCorp, referring to the stock rally.

Still, “for the stress test to have any sort of legitimacy, some of the banks are going to have to raise capital,” he said.